The amount of the charge stored in a battery is generally characterized by its state of charge, usually indicated by the initials SoC, which is defined as the ratio of the available capacity to the maximum possible capacity of the battery.
The knowledge of the SoC in a battery at a given moment is paramount for all systems which are powered by a battery, since their remaining autonomous operating time depends thereon. Unfortunately, it is impossible to measure the SoC directly. It is possible to use certain measurable physical quantities for which a relationship with the SoC is established. But the measurement of such quantities is governed by numerous constraints related to the environment of the battery and to the conditions of its use. For example, it is possible to use the no-load voltage; however, the conditions of measurement of this voltage remain limited to the periods during which the battery is not used. It is also possible to use the impedance of the battery; however, this quantity is greatly influenced by the experimental conditions such as the temperature and the current. Therefore, the state of charge of a battery can only be estimated during use with the aid of an appropriate model.
This estimation is substantially complicated by the fact that the state of charge of a battery depends on a multitude of parameters: the conditions of its use, that is to say its charge regime or discharge regime, the external temperature, on the intrinsic characteristics of the battery, etc. The calculation of the SoC does indeed depend on the maximum capacity Cmax of the battery, which may be considerably reduced if the external temperature is low. For example, the maximum capacity at a given instant may correspond to 80% of the maximum capacity measured under the more favorable conditions. Moreover, it decreases as the battery ages and makes it possible to establish an aging criterion called state of life (SoH).
Because of the technical and economic importance of the problem, very many schemes for estimating the state of charge of a battery have been proposed. Several of these schemes are described in the article by S. Piller, M. Perrin and A. Jossen “Methods for state-of-charge determination and their applications”, Journal of Power Sources 96 (2001) 113-120.
So-called “direct calculation” schemes rely on charts which match in a one-to-one manner the state of charge of a battery with another characteristic physical quantity of the battery, usually a voltage U measured across the terminals of the battery, and in particular the no-load voltage U0. See for example document U.S. Pat. No. 4,677,363. Unfortunately, a relation “SoC=f(U)”—where U is the voltage measured across the terminals of the battery—is not strictly one-to-one for all types of batteries, in particular, Li-ion batteries. Other physical quantities such as the no-load voltage U0, the physical properties of the electrolyte and the electrochemical impedance Z have been proposed for estimating the SoC. The relation SoC=f(U0), in particular, is reliable but rather inconvenient since the no-load voltage can only be measured when a battery has been in a rest state for a certain time and under specific temperature conditions. The physical properties of the electrolyte can only be measured when the latter is liquid and, consequently, they cannot be utilized for all types of electrochemical composition of the batteries. The relation SoC=f(Z) is not strictly one-to-one for all types of battery and varies greatly as a function of the temperature of the battery and of its charge/discharge regime. Furthermore, constructing charts for all the temperatures, all the aging states and all the discharge/charge regimes of a battery is a very laborious task requiring specific and expensive hardware. Moreover, these schemes do not make it possible to directly integrate the dispersion in the behaviors of the batteries of the same electrochemical composition. The inaccuracy in the measurements and the weak representation of the diversity of the behaviors of a battery afforded by charts do not make it possible to apply the technique of real-time direct calculation as is, but require calibration procedures that may entail a significant cost overhead.
Document US 2010/0090651 describes a method for estimating the state of charge of a battery comprising two steps:
firstly, a step of estimating the no-load voltage U0 by linear interpolation of voltage and current measurements;
then, a step of determining the state of charge on the basis of the value thus estimated of U0 by means of a chart.
To implement the first step, two different regression models are used depending on whether the battery is in a charging or discharging condition.
This method exhibits the aforementioned drawbacks of the direct calculation schemes, except in that it does not require a direct measurement of U0.
The estimation of the SoC based on physical models is the most widespread. This involves models which rely on variables such as a current, a voltage, an internal temperature, a no-load voltage, an external temperature, an impedance, etc. The simplest and best known way of estimating the SoC is “coulometry”, which consists in calculating the amount of charge CF/E provided by/extracted from a battery relative to the maximum capacity Cmax of the battery. The amount of charge CF/E is estimated by integrating the current I(t) during the use of the battery. The coulometric estimator of the SoC is expressed as follows:
                              S          ⁢                                          ⁢          o          ⁢                                          ⁢                      C            ⁡                          (              t              )                                      =                                            S              ⁢                                                          ⁢              o              ⁢                                                          ⁢                              C                0                                      +                                          C                                  F                  /                  E                                                            C                max                                              =                                    S              ⁢                                                          ⁢              o              ⁢                                                          ⁢                              C                0                                      +                                          1                                  C                  max                                            ⁢                                                ∫                                      t                    0                                    t                                ⁢                                                      η                    ·                                          I                      ⁡                                              (                        τ                        )                                                                              ⁢                                                                          ⁢                  d                  ⁢                                                                          ⁢                  τ                                                                                        (        1        )            where SoC0 is an initial state of charge, assumed known (for example, a state of complete charge or of complete discharge), [t0, t] is a period of use of the battery and η the Faraday efficiency (ratio of the charge which can be stored in the battery to the charge which can be extracted therefrom). See for example the article by Kong Soon Ng et al. “Enhanced coulomb counting method for estimating state-of-charge and state-of-health of lithium-ion batteries”, Applied Energy 86 2009) 1506-1511.
This scheme exhibits a certain number of drawbacks:
the current sensor may be inaccurate and, as the measured current is integrated, the measurement errors build up;
the knowledge of the maximum capacity is difficult within the framework of the application and may therefore be very approximate;
the phenomenon of self-discharge is not taken into account;
the Faraday efficiency is also not well known in real time.
The coulometric model for estimating the SoC can be improved by combining it with models of other measurable physical quantities by means of data fusion techniques such as Kalman filtering. This technique requires the construction of a model of the battery in the form of an equivalent circuit which depends on the electrochemical composition of the battery, and is therefore not generic.
Yet other schemes make it possible to estimate the SoC on the basis of models of the kinetics of the chemical reactions and of the diffusion phenomenon, which are specific to each type of electrochemical composition of the battery. The main drawback of these schemes is their lack of generality.
Finally, numerous other schemes for estimating the SoC use statistical training techniques to automatically determine coefficients of a physical, semi-physical or indeed purely mathematical model (approach of the “black box” type).
The article by T. Hansen and Chia-Jiu Wang “Support vector based state of charge estimator”, Journal of Power Sources 141 (2005), pages 351-358 and patent U.S. Pat. No. 7,197,487 describe a scheme for estimating the SoC on the basis of a kernel regression model with a polynomial kernel whose coefficients are estimated by the Support Vector Regression (SVR) scheme. Patent application US 2010/0324848 describes the use of a neural network—and of several mathematical techniques for estimating the coefficients of this network—to estimate the SoC of a battery on the basis of instantaneous measurements of voltage, current and temperature, and on the basis of the first and second derivatives of the voltage.
These schemes, based on statistical training, are potentially very general, since they use models which are not based on any assumption relating to the composition, the structure or the operation of the battery. Moreover these models are flexible since they can use a variable number of input variables and do not depend on the nature of the latter. However, the present inventors have realized that this great generality is difficult to achieve in practice. Indeed, the generality of a model depends in a critical manner on the quality of its training base, that is to say of the database used for the training of the coefficients of the SoC estimation model. This base must be sufficiently comprehensive without being redundant, and without its size becoming too big.